An ultra-incompressible ternary transition metal carbide

Abstract

The ternary transition metal carbide Mo_0.5W_0.5C was synthesized under high pressure and high temperature and the crystalline structure was confirmed by Rietveld refinements as being hexagonal (P6̄m2). The mechanical properties, bulk modulus and Vickers hardness were also investigated by in situ high-pressure X-ray diffraction and Vickers microhardness testing, respectively. The fitting bulk modulus of the ternary transition metal carbide is 399.9 ± 9.3 GPa, which is as compressible as diamond, and its asymptotic Vickers hardness is 15.3 GPa, nearly 60% harder than molybdenum carbide. The high bulk modulus is attributed to the high valence electron density and the greater hardness compared with γ-MoC is due to the strong bond between tungsten and carbon atoms.

---

Introduction

Up to now, a myriad of experiments and first principles calculations have been focused on refractory transition metal carbides and borides because of their extraordinary mechanical, electrical and catalytic properties.^1–5 Among the transition metal carbides, high-surface-area molybdenum carbides, employed in the conversion of methane to synthesis gas, are highly efficient catalysts which have been proven to be comparable to the noble metals, iridium and ruthenium.^6,7 Furthermore, molybdenum carbides are characterized by their relatively high bulk modulus and hardness and are widely used in applications where materials with high toughness and high wear resistance are much desired.^8,9

Generally, the above-mentioned prominent properties, especially the mechanical properties, are related to the crystal structure, electronic properties and stability of the carbides. Consequently, altering the crystal structure or the electronic properties may lead to an enhancement of the properties of these transition metal carbides. In the early study, ternary transition metal boride Os_0.5W_0.5B₂ was synthesized to study the change in mechanical properties, especially hardness, compared with binary transition metal boride. W and Os elements possessing different atomic radii lie near Re in the periodic table of elements, that is, an isoelectronic substitution. It is just the isoelectronic configuration that results in the same structure as ReB₂. The hardness of Os_0.5W_0.5B₂ is greater than that of the ternary borides WB₂ and OsB₂ and even close to that of ReB₂.¹⁰ To illustrate the effect of different valence electron radius on the mechanical properties of the transition metal compounds, Mo and W were selected because of their proximity in the periodic table and because they will crystallize with the same structure. The W and Mo atoms have nearly the same atomic radius, but the W atom has a relatively larger d electron orbital which will transform the electron configuration of γ-MoC; and this change will alter the properties of this compound. Within this context, we synthesized a ternary transition metal carbide, Mo_0.5W_0.5C, which has half of the molybdenum atoms substituted by tungsten. Interestingly, the measured bulk modulus and hardness testing indicate that this ternary carbide is ultra-incompressible and the hardness is almost 60% greater than that of molybdenum carbide.⁹ The hardness of this material was calculated using the obtained bulk modulus with Chen's hardness model and the result matches fairly well with the measured asymptotic Vickers hardness.¹¹

Experimental

Powders of pure molybdenum (99.95% in purity), tungsten (99.8% in purity) and amorphous carbon (99.5% in purity) at a ratio of 1 : 1 : 2 were ground together with an agate mortar and pestle until a uniform mixture was achieved. The powder mixture was pressed into a cylindrical sample, which was 6 mm in diameter and 2.5 mm in height, by means of a hydraulic press. The pellet was put into a hexagonal BN capsule which was used as an insulator material to prevent the starting material reacting with the carbon heater placed in a pyrophyllite cube. The synthesis experiment was carried out with a SPD6 × 600T cubic anvil apparatus. After the target pressure of 5.0 GPa was reached, the sample was first heated to 2000 K at the rate of 120 K s⁻¹, and kept at this target temperature for 20 to 60 min. Finally, the sample was quenched to room temperature by switching off the power supply. The pressure was given by a calibration curve that was established by determining the applied loads corresponding to the phase transformation pressures of bismuth, thallium and barium. The temperature was measured by a chromel–alumel type thermocouple placed in the center of the BN capsule. Powder X-ray diffraction patterns were collected with a D/MAX-RA type powder diffractometer, with Cu Kα radiation (λ = 1.5418 Å), voltage of 40 kV, and current of 30 mA. The compressibility of Mo_0.5W_0.5C was measured using high-pressure X-ray diffraction in a diamond anvil cell with methanol and ethanol (1 : 4) as the pressure medium. Diffraction patterns were collected to 48 GPa at the 4W2 beamline of Beijing Synchrotron Radiation Facility (BSRF). The samples were preliminarily polished using carbide silicon paper and then diamond polishing oil was used to obtain a mirror surface. The hardness of the samples was investigated using a HV-1000ZDT microhardness tester with a pyramid diamond tip, with a dwell time of 15 s. The residual indentation diagonal lengths were measured using a microscope under 400× magnification. Rietveld refinements were performed utilizing the GSAS program suite.¹²

Results and discussion

The powder X-ray diffraction pattern of Mo_0.5W_0.5C synthesized via high pressure and high temperature verifies that the compound is highly crystalline as shown in Fig. 1. The diffraction pattern matches fairly well with the existing reference data available for this material from the Joint Committee on Powder Diffraction Standards (JCPDS). The Rietveld refinements reveal that Mo_0.5W_0.5C is hexagonal (space group P6̄m2) and the refinements result is compiled in Table 1. The crystal structure for Mo_0.5W_0.5C exhibited in Fig. 2 possesses the following lattice parameters: a = b = 2.901 Å, c = 2.8424 Å. The ternary Mo_0.5W_0.5C crystallizes in the same structure as γ-MoC and WC, with mixed occupation of the transition metals. From the refined crystal structure picture, it is very clear that this ternary carbide crystallizes in an identical structure to γ-MoC and WC, with stacking of flat C layers separated by transition metal layers.

Fig. 1 Powder X-ray diffraction pattern of Mo_0.5W_0.5C powder in accordance with the reference pattern (JCPDS 65-8770).

Table 1 Details of the data collected and structure refinement of Mo_0.5W_0.5C

Compound	Mo0.5W0.5C
Radiation	Cu Kα
Crystal system, space group	Hexagonal, P6̄m2 (no. 187)
Lattice parameters a, b, c/Å	a = b= 2.9026, c = 2.830
Cell volume/Å^3	20.646
θ range/deg	20–90
Residuals	Rp: 0.0637
	Rwp: 0.0823
	χ^2: 1.630

---

Fig. 2 Crystal structure of Mo_0.5W_0.5C with mixed occupation of Mo and W atoms, showing Mo and W atoms as blue spheres and C atoms as gray spheres.

Transforming the electron configuration has been carried out by isostructure substitution to enhance the mechanical properties of γ-MoC. The hardness was measured because it is a representative parameter of mechanical properties. Vickers hardness was calculated according to eqn (1):

where P is the applied load, d is the arithmetic mean of the two diagonals of an indentation, and H_v is the Vickers hardness. At least five measurements were made on a sample at different loads ranging from 0.245 N to 4.9 N. The load-dependent Vickers hardness data for Mo_0.5W_0.5C are shown in Fig. 3. A minimum hardness of 15.3 GPa at 4.9 N and a maximum measured hardness of 23.2 GPa at 0.245 N were obtained, with the indentation image shown in Fig. 3. An inverse relationship between the applied load and the measured hardness has been extensively reported for many transition metal compounds. That is to say, the hardness displays a strong dependence on the applied load; this is called the indentation size effect. It is just for this reason that many hold that the Vickers hardness measured in this range is meaningless and that the asymptotic hardness ought to be the meaningful hardness.¹³ This behavior is largely attributed to the saturation of growth of microcracks in brittle materials, the recovery of smaller indentations and the strain gradient plasticity.^13–15 The asymptotic hardness of Mo_0.5W_0.5C, about 15.3 GPa, lies well below the generally acknowledged value of 40 GPa for superhard materials.

Fig. 3 Vickers hardness of pure sample measured as a function of applied load.

The bulk modulus measures the resistance of a material to volume change for a constant shape, and superhard materials usually possess an exceedingly high bulk modulus, though the inverse may not always be true – that is, an incompressible material is hard.^16–18 Thus, bulk modulus provides a rudimentary gauge in the search for potential hard materials. Investigation of the equation of state of Mo_0.5W_0.5C has been performed under hydrostatic compression up to 48 GPa, utilizing radial X-ray diffraction techniques in a diamond anvil cell (DAC). The synthesized material Mo_0.5W_0.5C is found to be stable up to the highest pressure of 48 GPa. Analysis of the high-pressure X-ray diffraction data results in the determination of the bulk modulus. The high pressure produced a remarkably tiny shift in peak positions shown in Fig. 4, demonstrating a small volume change, that is, a large bulk modulus. The pressure versus fractional volume data of Mo_0.5W_0.5C were fitted using the Birch–Murnaghan equation to gain the bulk modulus (B₀):

P = 3/2B₀[(V/V₀)^−7/3 − (V/V₀)^−5/3] × {1 − (3/4)(4 − B^′₀)[(V/V₀)^−2/3 − 1]} (2)

Fig. 4 X-ray diffraction patterns of Mo_0.5W_0.5C as a function of increasing pressure.

The bulk modulus was obtained with a value of 399.9 ± 9.3 GPa shown in Fig. 5(a) when the derivative of the bulk modulus with respect to pressure, B^′₀, was fixed to a value of 4, which is a canonical value to fit the state equation. This obtained bulk modulus value is remarkably high, exceeding the bulk modulus of tungsten tetraboride, rhenium diboride, osmium diboride, and boron nitride and close to the value of diamond of 442 GPa and tungsten carbide of 439 GPa.^4,14,19–22 Like a traditionally layered structure exhibiting extreme interlayer incompressibility, the crystallographic c-axis is less compressible than the a-axis and even exceeding that of diamond depicted in Fig. 5(b).²³ Considering the exceedingly high bulk modulus, we may expect that this material may have a high hardness value, similar to that of tungsten carbide or even close to the hardness of diamond. However, the measured result is that although the hardness is nearly 60% greater than that of γ-MoC, its hardness is well below the threshold of superhardness.

Fig. 5 (a) Pressure versus unit cell volume for Mo_0.5W_0.5C. Fitting these data with the Birch–Murnaghan equation of state results in a bulk modulus of 399.9 GPa when B^′₀ is fixed at the canonical value of 4. (b) Comparison of the individual lattice parameter compressibility with diamond. The a (olive) and c (blue) parameters are fitted with straight lines, while the diamond line (red) is taken from ref. 10.

In order to illuminate the inconsistency, the hardness of Mo_0.5W_0.5C is calculated with Chen's empirical hardness formula. According to Chen's hardness model, the Vickers hardness can be calculated as

H_v = 2(k²G)^0.585 − 3 (k = G/B) (3)

which can be used to predict the hardness of polycrystalline materials and bulk metallic glasses. The parameter k is Pugh's modulus ratio.¹¹ Based on the Vickers hardness formula, the calculated hardness of WC and γ-MoC is 30.4 and 12.1 GPa respectively (Table 2), which is consistent with the experimental value. Bulk modulus (B) and shear modulus (G) are two significant elastic properties correlated with the hardness, which are related by Poisson's value ν. In the case of isotropic metallic materials,

G = 3/2B(1 − 2ν)/(1 + ν) (4)

and the typical Poisson's value for the metallic materials is 0.3.²⁴ Based on the typical Poisson's value, the shear modulus is 184.2 GPa and the calculated Vickers hardness is 14.1 GPa, in good agreement with the asymptotic Vickers hardness. From the hardness calculation, it is apparent that the low hardness of this ternary transition metal carbide is induced by the low shear modulus, that is to say, strong metallic characteristics.

Table 2 Bulk modulus, shear modulus and Vickers hardness of different materials

Compound	B (GPa)	G (GPa)	Hexp (GPa)	Hcal (GPa)
Diamond	442 (ref. 21)	535 (ref. 17)	90 (ref. 25)	93.5 (ref. 11)
WC	439 (ref. 4)	282 (ref. 4)	30 (ref. 11)	30.4 (ref. 11)
γ-MoC	325.4 (ref. 8)	154.2 (ref. 8)	9.6 (ref. 9)	12.1
				13.4 (ref. 8)
Mo0.5W0.5C	399.9	184.6	15.3	14.1

---

These enhanced mechanical properties can be attributed to the bond strength that results from a stronger orbital hybridization of W–C compared with Mo–C when relativistic effects are taken into account.²⁶ Based on Einstein's relativity theory, the 5d valence electron orbital of tungsten increases in energy and expands. The orbital change of the 4d valence electron of molybdenum is insignificant because this effect becomes significant for Z equal to or larger than 50.^27,28 Though tungsten and molybdenum have exceedingly similar atomic radii, tungsten has a greater d electron orbital compared with molybdenum which increases the overlap of the electron.²⁹ It is just this greater overlap that results in a strong W–C bond. Considering this material has the same crystal structure, adding the stronger W–C bonds will resist the collapse when an external force is applied to the sample surface.

Furthermore, considering that tungsten and molybdenum have the same valence electron, we may expect that Mo_0.5W_0.5C, WC and γ-MoC have similar bulk modulus. The measured bulk modulus of WC and Mo_0.5W_0.5C is similar, but far greater than that of γ-MoC. We speculate that the inner orbital electrons may play some role in resisting the volume change under extreme pressure.²⁶ Consequently, the bulk modulus of this ternary carbide will be larger than that of γ-MoC and this phenomenon can also be verified by other 4d and 5d transition metal carbides, borides and nitrides.^{10,26,30–33} Substitution of half of the Mo atoms results in a drastic increase of the bulk modulus, whereas the shear modulus of the ternary carbide turns out to have little relation to the valence electron density.

Conclusions

In summary, the ternary transition metal carbide Mo_0.5W_0.5C has been synthesized under high pressure and temperature. The strong metallic characteristics lead to low hardness, though the bulk modulus is exceedingly high. The measured Vickers hardness of Mo_0.5W_0.5C is nearly 60% greater than that of γ-MoC, which may be attributed to the stronger bond strength stemming from greater electron overlap of d electron and p electron. The higher valence electron density of 5d transition metal carbides compared to 4d transition metal carbides leads to the dramatic increase of the bulk modulus, which has little dependence on the structural details.

Acknowledgements

Project supported by the National Basic Research Program of China (grant no. 2011CB808200), the Program for Changjiang Scholars and Innovative Research Team in University, China (grant no. IRT1132), and the National Natural Science Foundation of China (grant no. 51032001, 11074090, 10979001, 51172091, 11104103 and 51025206).

References

1. R. B. Kaner, J. J. Gilman and S. H. Tolbert, Science, 2005, 308, 1268.
2. H. Y. Chung, M. B. Weinberger, J. B. Levine, A. Kavner, J. M. Yang, S. H. Tolbert and R. B. Kaner, Science, 2007, 316, 436.
3. A. Šimůnek and J. Vackář, Phys. Rev. Lett., 2006, 96, 085501.
4. F. M. Gao, J. L. He, E. D. Wu, S. M. Liu, D. L. Yu, D. C. Li, S. Y. Zhang and Y. J. Tian, Phys. Rev. Lett., 2003, 91, 015502.
5. X. J. Guo, L. Li, Z. Y. Liu, D. L. Yu, J. L. He, R. P. Liu, B. Xu, Y. G. Tian and H. T. Wang, J. Appl. Phys., 2008, 104, 023503.
6. J. B. Claridge, A. P. E. York, A. J. Brungs, C. Marquez-Alvarez, J. Sloan, S. C. Tsang and M. L. H. Green, J. Catal., 1998, 180, 85.
7. M. D. Scanlon, X. J. Bian, H. Vrubel, V. Amstutz, K. Schenk, X. L. Hu, B. H. Liu and H. H. Girault, Phys. Chem. Chem. Phys., 2013, 15, 2847.
8. Y. Z. Liu, Y. H. Jiang, J. Feng and R. Zhou, Phys. B, 2013, 419, 45.
9. E. J. Saur and H. D. Schechinger, IEEE Trans. Magn., 1981, 17, 1029.
10. Q. F. Gu, G. Krauss and W. Steurer, Adv. Mater., 2008, 20, 3620.
11. X. Q. Chen, H. Y. Niu, D. Z. Li and Y. Y. Li, Intermetallics, 2011, 19, 1275.
12. A. C. Larson and R. B. Von Dreele, GSAS., LANSCE, MS-H805, Los Alamos National Laboratory, Los Alamos, NM 87545, LAUR 86–748, Vers. 2000.
13. V. Brazhkin, N. Dubrovinskaia, M. Nicol, N. Novikov, R. Riedel, V. Solozhenko and Y. Zhao, Nat. Mater., 2004, 3, 576.
14. R. Mohammadi, A. T. Lech, M. Xie, B. E. Weaver, M. T. Yeung, S. H. Tolbert and R. B. Kaner, Proc. Natl. Acad. Sci. U. S. A., 2011, 108, 10958.
15. V. V. Brazhkin, A. G. Lyapin and R. J. Hemley, Philos. Mag. A, 2002, 82, 231.
16. J. J. Gilman, R. W. Cumberland and R. B. Kaner, Int. J. Refract. Met. Hard Mater., 2006, 24, 1.
17. D. M. Teter, MRS Bull., 1998, 23, 22.
18. A. Y. Liu and M. L. Cohen, Science, 1989, 245, 841.
19. W. Zhou, H. Wu and T. Yildirim, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 76, 184113.
20. R. W. Cumberland, M. B. Weinberger, J. J. Gilman, S. M. Clark, S. H. Tolbert and R. B. Kaner, J. Am. Chem. Soc., 2005, 127, 7264.
21. H. J. McSkimin and P. Andreatch Jr, J. Appl. Phys., 1972, 43, 2944.
22. J. Q. Qin, D. W. He, J. H. Wang, L. Fang, L. Lei, Y. J. Li, J. Hu, Z. L. Kou and Y. Bi, Adv. Mater., 2008, 20, 4780.
23. J. B. Levine, S. H. Tolbert and R. B. Kaner, Adv. Funct. Mater., 2009, 19, 3519.
24. J. Haines, J. Léger and G. Bocquillon, Annu. Rev. Mater. Res., 2001, 31, 1.
25. Y. J. Tian, B. Xu and Z. S. Zhao, Int. J. Refract. Met. Hard Mater., 2012, 33, 93.
26. M. B. Weinberger, J. B. Levine, H. Y. Chung, R. W. Cumberland, H. I. Rasool, J. M. Yang, R. B. Kaner and S. H. Tolbert, Chem. Mater., 2009, 21, 1915.
27. G. C. Bond, Platinum Met. Rev., 2000, 44, 146.
28. J. Onoe, R. Sekine, K. Takeuchi, H. Nakamatsu, T. Mukoyama and H. Adachi, Chem. Phys. Lett., 1994, 217, 61.
29. D. C. Hoffman and D. M. Lee, J. Chem. Educ., 1999, 76, 331.
30. I. R. Shein and A. L. Ivanovskii, J. Phys.: Condens. Matter, 2008, 20, 1.
31. H. P. Liermann, A. K. Singh, M. Somayazulu and S. K. Saxena, Int. J. Refract. Met. Hard Mater., 2007, 25, 386.
32. L. López-de-la-Torre, B. Winkler, J. Schreuer, K. Knorr and M. Avalos-Borja, Solid State Commun., 2005, 134, 245.
33. P. P. Liu, F. Peng, S. Yin, F. M. Liu, Q. M. Wang, X. H. Zhu, P. Wang, J. Liu and D. W. He, J. Appl. Phys., 2014, 115, 163502.

---